integral (cos x)^2 dx

vadik

Do any one have an idea how to calculate integral of (cos x)^2 ? Or is it even possible? I tried some substitutions and/or rules of trigonometry, like cosxcosx+sinxsinx=1, but it didn't help. Thank you!

mathman

cos²x+sin²x=1
cos²x-sin²x=cos2x
Therefore cos²x=(1+cos2x)/2

I'll let you finish.

vadik

Thank you. :) integral (cos x)^2 dx

mussgo

dont you have to use half angle identities to get integral of cos^2 ?

HallsofIvy

No, double angle formulas as mathman said.

jacobrhcp

an easy way to remember the solution to this common integral, when integrating over a whole period:

cos^2 x + sin ^2 x =1
[tex] \int cos^2 x = \int sin^2 x [/tex]
, at least when you integrate over a whole period

[tex] \int cos^2 x + \int sin^2 x =[/tex] length of a period

so the integral gives length of a period divided by 2

awvvu

Why does this thread have over 16,000 views?

edit: Oh, it's four years old.

ohhohh

First use the half-angle formula to change the cos(x)^2 to (1+cos(2x))/2...
This will allow you to break the integral into two seperate problems much easier to solve
integral{ 1/2dx + integral{ cos(2x)dx
Then you will have x/2 + (sin(2x)/2) + C

snipez90

What the, that's not even correct. If you're gonna revive a 5-year old thread, at least make sure you don't have arithmetic errors.

chislam

sin(2x)/4 ;)

abhishek2208

use the euler's formula

cos x= [e^ix+e^-ix ]
[-------------]
[ 2 ]

sponsoredwalk

http://www.5min.com/Video/An-Introdu...sine-169056088

Why doesn't the student, after nearly 6 years of unsuccessfully attempting this crazy integral, try a visual aid?

Redbelly98

This is crazy. The very first reply, post #2, answered the question. Six years ago!